Determination of resistivity profiles in anti-corrosion coatings from constant-phase-element parameters

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OULOUSE

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uverte (

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To link to this article : DOI : 10.1016/j.porgcoat.2013.12.013

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To cite this version :

Musiani, Marco and Orazem, Mark E. and

Pébère, Nadine and Tribollet, Bernard and Vivier, Vincent

Determination of resistivity profiles in anti-corrosion coatings from

constant-phase-element parameters. (2014) Progress in Organic

Coatings, vol. 77 (n° 12). pp. 2076-2083. ISSN 0300-9440

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Determination

of

resistivity

profiles

in

anti-corrosion

coatings

from

constant-phase-element

parameters

M.

Musiani

a

_,

_M.E.

_Orazem

b

_,

_N.

_Pébère

c,∗

,

B.

Tribollet

d

_,

_V.

_Vivier

d a_{Istitutoperl’EnergeticaeleInterfasi,ConsiglioNazionaledelleRicerche,35127Padova,Italy}

b_{DepartmentofChemicalEngineering,UniversityofFlorida,FL32611,USA}

c_{UniversitédeToulouse,CIRIMAT,UPS/INPT/CNRS,ENSIACET,4,alléeEmileMonso–BP44362,31030Toulousecedex4,France} d_{LaboratoireInterfacesetSystèmesElectrochimiques,UPR15duCNRS,UniversitéPierreetMarieCurie,75252Pariscedex05,France}

Keywords: CPE Electrolyteuptake Impedancemodelling Pores

a

b

s

t

r

a

c

t

ArecentlyproposedmodelwhichexplainstheCPEresponseexhibitedbymetal/coating/electrolyte sys-temsastheresultofpower-lawdependencesofthecoatingresistivityandpermittivityalongtheir thicknessisrevisitedandappliedtothreedifferentcoating/electrolytecombinations.Itisshownthat resistivityprofilesmaybedetermined,andtheirevolutionwiththetimeofexposuremaybefollowed. Theeffectoftheassumptionsmadeoncoatingandelectrolyteresistivityontheregressedparameters isdiscussedandthefactorswhichaffectthereliabilityofthemeasuredwateruptakearehighlighted. Itisshownthatboththecompositionofthecoatingandthatofthetestsolutionsinfluencethetime dependenceofthecoatingperformance.

1. Introduction

Electrochemicalimpedancespectroscopyisapopulartechnique for the assessment of the corrosion protection performance of organiccoatings.Theanalysisofimpedancedataisoftenbasedon theequivalentcircuitproposedbyBeaunieretal.[1]inwhichthe coatingcapacityandthedoublelayercapacityarereplacedby con-stantphaseelements(CPE),theimpedanceofwhichisZ=1/(jω)˛_Q.

SubstitutionofCPEsforcapacitiesmaystronglyimprovethe qual-ityofthefittingbetweentheexperimentaldataandtheequivalent circuit,butcreatesambiguitiesinthephysicalinterpretationofthe results,sinceQcannotbesimplyidentifiedwiththecoating capac-ity[2]andcannotbedirectlyusedtocalculatethewateruptakein thecoatingthroughtheBrasherandKingsbury[3]approach. Vari-ousformulashavebeenproposedforthecalculationoftheeffective capacityfromCPEparameters[4,5],buttheirapplicationrequires knowledgeofthephysicaloriginoftheCPEbehaviour[2,6].

In a recent paper [7], our group has shown that the CPE behaviour observed in theimpedance of a coated systemmay beexplainedby aninhomogeneouselectrolyteuptake if(i)the electrolytevolumefractiondecreasesfromthecoating/electrolyte interfacetothemetal/coatinginterfaceaccordingtoapower-law and(ii)theresistivityandpermittivityofthesystemarecalculated usingeffectivemediumtheoryformulascorrespondingtoa par-allelcombinationofcoatingmaterialandelectrolyte.Thismodel,

∗ Correspondingauthor.Tel.:+33534323423;fax:+33534323499.

E-mailaddress:Nadine.Pebere@ensiacet.fr(N.Pébère).

henceforth briefly called “power-law model”was compared to experimentaldataobtainedwithahybridsol–gelcoatingexposed toa0.5MNaClsolution.Itwasconcludedthat,asaresultofthe progressiveelectrolyteuptake forincreasingexposuretime, the resistivityofthecoatingmarkedlydecreased(afteroneweek,the decreaseatthecoating/electrolyteinterfaceattainedca.6ordersof magnitude,withrespecttothedrycoating),whileitspermittivity remainedpracticallyunchanged.Furthermore,itwasshownthat thenumberand/orsectionofthethroughpores,i.e.poresasdeep asthewholecoatingthickness,directlyconnectingtheelectrolyte withthemetalunderneaththecoatingthroughalow-resistance path, increased with exposure time. These results allowed the extension ofa previously derived model [8,9]appliedso farto passiveoxidesandhumanskin[10],toanti-corrosioncoatings.

Thepresentpaperaimsatextendingtheinvestigationdescribed inRef. [7],focusingmainlyonthreeissues:(i)theeffectof the assumptions madeoncoating and electrolyteresistivity onthe regressed parameters; (ii)the analysis of the relative amounts of electrolytewithin throughand shortpores; (iii) theanalysis ofexperimentaldatarelevanttoothercoating/electrolyte combi-nations,basedonthepower-lawmodel,andadiscussionofthe differentbehaviourofdifferentsystems.

2. Experimental

Adescriptionofthecoatings,theirmethodofpreparation,and theelectrochemicaltechniquesusedfortheircharacterizationare presentedinthissection.

ξ = 1 ξ = 0 Electrolyte Coang Substrate ρ(ξ) ε(ξ) R_pore R_e CPE Oxide Zc

Fig.1.Schematicrepresentationofasubstrate/oxide/coating/electrolytesystem.Reistheuncompensatedelectrolyteresistance;Rporeaccountsforthethroughporesjoining

thecoating/electrolyteandcoating/oxideinterface;Zcistheimpedanceoftheelectrolyte-penetratedcoatingdescribedbyEq.(3);theCPErepresentstheoxidelayercovering

theAl2024alloy.

2.1. Hybridsol–gelcoatings

Twocoatingswereprepared.Forbothsystems,the organosilox-ane sol was prepared by using 3-glycidoxypropylethoxysilane (GLYEO),tetraethylorthosilicate(TEOS)andbutanol.Afirst solu-tionwasmadebyaddingapolyaminoamide(PAA)tothesol,with aGLYEO/TEOS/PAAmassratioof3:1:2.Thesolutionwasprepared withanexcessoforganosilane,thereforetheresultingcoatingwas calledO.Theprocesstakesadvantageofthetwomoietiesofthe organosilane molecule(GLYEO). Theorganicpart of theGLYEO reactswiththeaminefunctionsofthePAAtodeveloptheorganic partofthehybridcoating,whilethesilanepartundergoestheusual hydrolysisandcondensationstepsofsol–gelsynthesis,toforma silicon-basednetwork.TEOSwasaddedtoincreasethecoating den-sity.Inthesecondsolution,anepoxycompoundwasaddedtothe firstsolution,withaGLYEO/TEOS/PAA/Epoxyratioof1:1:10:8.Due tothepresenceofanepoxyinthesolution,theresultingcoating wascalledsampleE.Theadditionoftheepoxycompoundinthe liq-uidsol–gelresinrequiredadifferentprocedureformixingtogether thecompounds.Forthisreason,sampleEisnotcomparable,from achemicalpointofview,withsampleO.Thesol–gelfilmsdidnot containanypigmentsorfillers.

Thecoatingsweredepositedontoa2024T3aluminiumalloy currentlyusedintheaerospaceindustry.Thespecimensconsisted of125mm×80mm×1.6mmplatesmachinedfromrolledplate. Beforepainting,thesamplesweredegreasedat60◦_C(pH=9)for

15min,rinsedtwicewithdistilledwater,thenetchedinanacid bathat52◦_{Cfor10min,andrinsedagainwithdistilledwater.The}

liquidpaintswereappliedbyairsprayingandcuredat100◦_Cfor

1h.Thecoatingsthicknesswasmeasuredatseverallocationsfrom theobservationofthecross-sectionsofthesamplesbySEMand foundtohaveanaveragevalueof20±2mm.

2.2. Electrochemicalimpedancemeasurements

Athree-electrodeelectrochemicalcellwasusedinwhichthe coated specimenservedas theworkingelectrode. Acylindrical Plexiglastubewasassembledontopofthecoatedsample, expos-ingasurfaceareaof24cm2_{.Alargeplatinumsheetwasusedas}

counter-electrode.Asaturatedmercury/mercuroussulphate ref-erence electrode was used for electrolytes containing Na2SO4,

and a saturated calomel reference electrode wasused in elec-trolytes containing NaCl. The electrochemical cell wasopen to air and was kept at room temperature withan average value of 17◦_{C and which may have undergonefluctuations by±2}◦_C.

Followingourpreviouswork,theresultingvariationsinthe dielec-tric constant of water were unlikely to have significanteffects on the experimental impedance response [9]. Electrochemical impedancemeasurementswerecarriedoutusingaBiologicVSP apparatus.Theimpedancediagramswereobtainedunder potentio-staticconditionsatthecorrosionpotentialoverafrequencyrange of60kHz–10mHzwith6pointsperdecade,usinga20mV peak-to-peaksinusoidalvoltage.Theelectrochemicalbehaviourofthe coatingswascharacterizedineither0.5MNa2SO4 or0.5MNaCl,

forexposuretimesrangingfrom2hto168h.TheNa2SO4solution

wasusedtoachieveabetterknowledgeoftheintrinsic proper-tiesofthecoatingsbecausetheevolutionofthesystemwasslower thaninNaClsolution.TheresultsconcerningsampleEintheNaCl solutionwerepreviouslyreportedinRef.[7].

3. Modelfordataanalysis

Themodelemployedforthedataanalysishasbeenpreviously described [7];onlya briefsummaryis reportedhere.Ascheme ofasubstrate/oxide/coating/electrolytesystem,anditsequivalent circuit,arepresentedinFig.1.Theimpedanceisassumedtoconsist ofthreecomponentsconnectedinseries:

i.theuncompensatedelectrolyteresistance; ii.theimpedanceofthecoating,discussedbelow;

iii.theimpedance oftheoxidecovering theAl2024alloy;this impedanceisaccountedforbyaconstantphaseelement(CPE) andisnolongerdiscussedinthefollowing.

Thecoatingisassumedtobepenetratedbytheelectrolytewhich fillsitspores.TheseporesarerepresentedinFig.1asbeingstraight, althoughtheymaybetortuousandhavevariablelateral dimen-sion.Allporeshaveamouthatthecoating/electrolyteinterface, butonlyafew(henceforthcalled“throughpores”)areasdeepas thecoatingandreachthecoating/oxideinterface,providinga low-resistivitypath,withresistanceRpore,betweentheelectrolyteand theoxide.Theotherpores(henceforthcalled“shortpores”)areless deepthanthecoatingthicknessı,andthusdifferentplanesparallel totheinterfaces,locatedwithinthecoatingatdifferentpositions =x/ı,crossdifferentnumbersofpores(seesketchinFig.2),and differentelementallayersofthecoating,dthick,havedifferent localelectrolytevolumefractions().Sucharepresentationofthe electrolyte-penetratedcoatingisinagreementwiththeone pro-posedbyMiˇskovi ´c-Stankovi ´cetal.[11,12]onthebasisofoptical microscopycoupledwithimageanalysis.

Fig.2. Schematicrepresentationofthinlayersofthecoatingmateriallocatedat differentpositions,highlightingthatthenumberofporesdecreasesasbecomes smaller,i.e.asthedistancefromthecoating/electrolyteinterfaceincreases.

Theelectrolytevolumefractionaffectsthelocalresistivityand permittivityofthecoating,whichareexpressedthrougheffective mediumtheoryformulasas

()−1=−1_w()+−1_c [1−()] (1)

and

ε()=_εw()+_εc[1−_()] (2)

wherethesubscriptswandcrefertotheelectrolyteandthe coat-ingmaterial,respectively.Eqs.(1)and(2)takeintoaccountthat, ineachelementallayerparalleltotheinterfaces,eachpositionis occupiedbyeitherthecoatingmaterialortheelectrolyte,andso thesetwomediaareinparalleltoeachother.Inthis approxima-tionitisunimportantwhether()istheresultofthepresenceof alargenumberofsmallerporesorasmallnumberoflargerpores. However,()doesnottakeintoaccountthewaterpresentwithin thecoatingasindividualmoleculesinteractingwithpolymeric net-workandnotformingaggregatesbigenoughtoallowdissolution ofsaltsandgenerateaconductivemedium.Suchpolymer-bounded waterhasbeenreportedtobea verysignificantfractionofthe totalwater uptakenbyepoxycoatings[11]andtocausestrong plasticizationofanepoxy/polyamidoaminecoating[13].Therefore, thewateruptakedeterminedthroughtheanalysisofexperimental databycomparisonwiththemodelproposedinRef.[7]islikely tobeunderestimated.Inafollowingsection(seeSection4.1.3),it willbediscussedhowalowerresistivityoftheelectrolytewithin thepores,ascomparedtothatoftheexternalsolution,maybea furthercauseforunderestimatingthewateruptake.

Under assumption that each elemental layermay be repre-sented by a parallel combination of a resistance ()d and a capacitanceε()ε0/d,theimpedanceoftheelectrolyte-penetrated

coating(Zc)iscalculatedas Zc(ω)=ı 1

Z

0 1 ()−1+_jωε()ε0d (3)

Thecontributionofporesthatextendtotheoxidesurfaceis includedseparatelyfromthedevelopmentofEq.(3).Theoverall

impedanceZ(ω)ofthecoatingistherebygivenbythepore resis-tanceRporeinparallelwithZc,i.e.

Z(ω)=[Zc(ω)−1+R−1 pore]

−1

(4) Toaccountfortheprogressivevariationinthenumberofpores along the coating thickness, the hypothesis is made that () changesfrom(0)=0at=0to(ı)at=1accordingtoa power-law,i.e.,

()= (ı)

1+(ı)( −1) (5)

ThecoatingpartcorrespondingtotheimpedanceZc contains only“shortpores”,meaningthatnoelectrolytereachesthe inter-facebetweenthecoating andtheoxideand, asa consequence, (0)=0.

In Ref. [7], calculated impedanceplots were presented with (ı)andRpore asparameters.It wasshownthat,accordingtoa moregeneraltheoryreportedinRef.[8],Z(ω)correspondedtoa CPEbehaviour,withaCPEexponent ˛linkedtothepower-law exponent bytheequation

˛= −1

(6)

ItwasshowninRef.[7]thatfittingtheabovedescribedmodel toexperimentaldataalloweddeterminationof ,(ı),andRpore, byassumingknownorreasonablevaluesforw,c,εwandεc.The ()−profileswerecalculatedbyenteringthefitted and(ı) valuesintoEq.(5);hence,()−_profilescorrespondingto differ-entimmersiontimeswereobtainedthroughEq.(1).Theseprofiles, presentedinRef.[7],neglectedthethroughpores,and,therefore,at allimmersiontimes,(0)wasidenticaltoc.Inthepresentpaper, theelectrolytecontentinthethroughporesiscalculatedas ϕpore=Vpore V_film = Apore A_film = ıw RporeAfilm (7) where Vdenotes a volume, and Ais a surface area(with Rpore normalizedtounitsurfaceareaandAfilm=1cm2).Thisallows esti-mationofthefractionoftheuptakenelectrolytethatiscontained inthethroughporesandcalculationof()−_profiles,takinginto accountallpores.Owingtotheassumedcylindricalgeometryof thethroughpores,Rporeisnotafunctionofposition.

Theabovedevelopmentretainsthemeaningof(0)asthe resis-tanceof thedrycoating,c.Asmaybeseenin thesubsequent discussionofexperimentalresults,thepower-lawmodeldoesnot accountadequatelyforthehigh-frequencyresponse.Theoriginof thisdiscrepancyis,asyet,unknown.Atentativeexplanationmight invokecapacitiveinteractionsbetweenadjacentpores.The regres-sionanalysiswastherefore performedfor frequenciesuptoan upperlimitwhich,fordifferentsystems,variedfrom0.5to5kHz (seeFigs.3and6).

4. Resultsanddiscussion

Theresultsarepresentedintermsoftheinfluenceofassumed valuesforparametersw,c,εwandεconthefittedparameters,the relativeamountsofelectrolytewithinthroughandshortpores,and theinfluenceofcoatingformulationandelectrolytecomposition.

4.1. Effectofw,c,εwandεconfittedparameters

Coatedsampleswereprepared,andimpedancemeasurements wereperformedasdescribedinSection2.Foreachcombination of coating/electrolytic solution/immersion time the experimen-taldatawerecomparedwiththemodelshowninFig.1,usinga non-commercialsoftwaredevelopedattheLISECNRS,Paris.This

Fig.3.ComparisonoftheexperimentalimpedanceplotsobtainedwithsampleEexposedto0.5MNaCl,aftera48-himmersiontime,withthebestfittedcurvescorresponding tothecvaluesindicatedontheNyquistplot.

softwareallowedregressionofthemodelconsistingofa combina-tionofpassivecircuitelements,likeRpore,theelectrolyteresistance andtheCPEparametersrelevanttotheoxidefilm,andtheanalytical expressionofZc(ω),butdidnotprovideconfidenceintervalsforthe bestfittedparameters.Inourpreviouswork[7],itwasexplained that,owingtothequasi-capacitiveblockingbehaviourobserved atlowfrequency,theoxidefilmresistancecouldbeassumedto beverylargeandthereforeitsinclusionintheequivalentcircuit,in parallelwiththeCPE,wasnotnecessary.Equallyunnecessarywere circuitelementsaccountingforthecorrosionreactions,becauseno signofcorrosionwasobservedfortheimmersiontimesexplored inthepresentinvestigation.

In theregressionprocedure, , (ı)andRpore weretheonly adjustableparametersforthecoating;whereas,w,c,εwandεc weregivenfixedvalues(w=2.22×101_cm,

c=2×1011_cm,

εw=82 and εc=8). In our previouspaper [7] the effect of the assumedvaluesonthefittedparameterswasnotdiscussed.New dataandamoredetaileddiscussionarepresentedbelow.

4.1.1. Parametersεwandεc

Thepermittivities(εwandεc)areknownwithrathergood pre-cision;furthermore,ithasbeenshownthattheε()−_profilesare quiteflatandthereforedonotaffecttheimpedanceofthesystem inasignificantway[9].

4.1.2. Parameterc

Theresistivityofthedrycoatingcislesswell-known.Thus, rec-ognizingthatitisimportanttoassessthemagnitudeofitseffect, themodelwasregressedtothesamesetofdatabyassumingin eachrunadifferentcvalue,coveringaratherwiderange.Fig.3 shows,asanexample,anexperimentalimpedanceplot,obtained withsampleE immersedin 0.5MNaClaftera 48-himmersion time,comparedwith7bestfitteddiagramscorrespondingtoc valuesvaryingfrom1010_cmto2×1013_{cm.Inallcases,the}

agreementbetweenexperimentalandcalculatedcurvesisgoodat allfrequencies(withsomedifferencesatfrequenciesabove5kHz where,asdiscussedabove,themodelisnotfullysatisfactory).Fig.4

showsthatthefittedparameters ,(ı)andRporedonotdepend oncinasignificantway,solongasc>5×1010_cm.Many

poly-mericmaterialshavearesistivityhigherthanthisthresholdvalue

[14],possiblybysomeordersofmagnitude.Forexample,a resis-tivityof1×1015_{cmhasbeenreportedforadrynylonfilm[15].}

Alltheresultspresentedinthefollowingsectionswereobtained byassumingc=2×1011cm,asinourpreviousstudy[7]andin

otherstudies[16].

4.1.3. Parameterw

Themostobviousassumptionaboutw,madebyourselvesin Ref.[7]andinthepresentstudyandbyotherauthors,e.g.[11], isthatitisidenticaltotheresistivityoftheelectrolyticsolution usedintheimpedancemeasurement.Thisimpliesthatthe com-positionof theelectrolyte insidetheporesshouldbe thesame as its bulk composition or, in otherwords that the water and theionsdissolvedinitbeincorporatedintothecoatingwithout anyselectivity.Resultspresentedintheliteratureshowthatsuch an assumptionmight not becorrect forall systems.For exam-ple,CastelaandSimoes[17]mentionthatthediffusivityofions islowerthanthatofwater;Huetal.[18]reportthatthe diffusiv-ityofchlorideioninepoxycoatingsisca.3ordersofmagnitude lowerthanthediffusivityofwater;and,accordingtoMiˇskovi ´c-Stankovi ´cetal.[11],theratiobetweenthediffusivitiesofwater andchlorideionisslightlyhigherthan10.Thus,wateruptakemay precedeionsuptake[11,12],and,solongasequilibriumisnotyet reached,thesolutionintheporesislikelytobelessconcentrated thantheoutersolution.Itisalsoquitepossiblethatthe compo-sitionoftheelectrolytewithintheporeswouldbeafunctionof immersiontime.Thechemicalnatureoftheelectrolyte,especially itsanion,mayhaveimportanteffects onthecoatingbehaviour.

1010 1011 1012 1013 0 1 2 3 4 5 γ / d im e n s io n le s s ρ_c / Ω cm

a

1010 1011 1012 1013 0.0 1.0x10-5 2.0x10-5 3.0x10-5 φ (δ ) / d im e n s io n le s s ρ_c / Ω cm

b

1010 1011 1012 1013 0 1x105 2x105 3x105 4x105 5x105 Rp o re / Ω cm ρ_c / Ω cm

c

Fig.4.Effectoftheassumedcvalueonthebestfittedparameters (a),(ı)(b)

andRpore(c).

Duarteetal.[19],usingnegative-feedbackscanning electrochem-ical microscope,have observed various topographic changes in coatingsduetothewateruptakeandtheingressofdissolvedions dependingontheelectrolytecomposition.

It isnoteworthythat thepermselectiveuptake of asolution lessconcentrated thanthebulksolutionwouldhave significant consequenceson(i)thedeterminationofthe()valuesand(ii) thecomparisonofdifferentelectrolytes.Sincecistypically8–10 ordersofmagnitudelargerthanw,Eq.(1)reducesto

()−1=_−1_w() (8)

already for very low () values. If an incorrectly low w is assumed,thewateruptakeisunderestimatedbythesamefactor,

1.0 0.8 0.6 0.4 0.2 0.0 104 105 106 107 108 109 1010 1011 1012 24 h 72 h 168 h

ρ

(

ξ

)

/

Ω

cm ξ / dimensionless

Fig.5. ComparisonoftheresistivityprofilescalculatedforthecoatingE/NaCl solu-tionsystem,calculatedonthebasisoftotalwateruptake(emptysymbols)orwater uptakeinshortporesonly(fullsymbols).Immersiontimesareindicatedonthe figure.

becauselargeramountsoflessconcentratedelectrolyticsolution are required toachieve a fixed() value.The permselectivity effectsmaybemoreorlessmarkedfordifferentsaltsand,thus,may affecttheestimatedwateruptaketoadifferentextent.Miˇskovi ´c-Stankovi ´cetal.[12]reportedthatthewaterdiffusivityinepoxy coatingsdidnotdependonnatureoftheanion(chloride,sulfate, naphtol-3,6-disulphonate).Sincetheseanionshavethemselves dif-ferentdiffusivities,differentelectrolyteconcentrationsshouldbe foundintheporesofcoatingsimmersedinelectrolytesofthesame molarity,butwithdifferentanions.Inturn,differentelectrolyte concentrationswouldcausedifferentresistivityprofilesand dif-ferentimpedanceresponses.

4.2. Electrolyteinshortandthroughpores

The volume fraction of the electrolyte within the through pores,henceforthdenotedpore,wasdeterminedfordifferent coat-ing/electrolytecombinationsandvariousimmersiontimesusing Eq.(7)andthefittedRporevalues.Table1reports,asanexample, datarelevanttocoatingEin0.5MNaCl.Thesametablereportsalso thefittedparameters(ı), ,andRporeandthevolumefractionof theelectrolyteintheshortpores,averagedalongthecoating thick-nessı,henceforthdenotedav.Itmustbeemphasizedthat,ifwis underestimated,forthereasonsdiscussedintheprevioussection, bothporeandavwillbeunderestimatedbythesamefactor,and theirratiowillbecorrectlyassessed.InspectionofTable1shows that,forallimmersiontimes,av>pore,andthereforemostofthe electrolyteiscontainedinporesthatdonotreachthemetal. How-ever,thepore/avratioincreasesastheimmersiontimeincreases. Thissuggeststhat,forthissystem,astheimmersiontimeis pro-longedand thewateruptake progresses,(i)thenumber and/or diameteroftheporesincreasesand(ii)theporedepthincreases, suchthatanumberofshortporesbecomethroughporesatlonger immersiontime.Alltheseconclusionsagreewiththosedrawnby Miˇskovi ´c-Stankovi ´cetal.[11]fromtheanalysisofresultsofliquid sorptionandthermogravimetricexperiments.

Itisworthpointingoutthatthecalculationwasmadefor cylin-drical pores,perpendicular to the interfaces, which allows the volumeratioinEq.(7) tobereplacedbythesurfacearearatio. Clearly,realporesmustbetortuous.Consideringtheirtortuosity wouldaffectpore(becauseahighertortuositywouldcorrespond toahigherapparentıandthereforeahigherpore),butnotav (becauseEqs.(1)and(2)holdforanyporegeometry).Unless tortu-osityvaluesaremuchhigherthanafewunits,theconclusionthat av>porestillholds.

Table1

Dependenceofthefittedparameters(ı), andRporeandofthecalculatedquantitiesavandporeontheimmersiontimein0.5MNaClforcoatingE.

Immersiontimein0.5MNaCl/h (ı)/dimensionless /dimensionless Rpore/cm2 av/dimensionless pore/dimensionless

24 1.5×10−5 _{3.5 1.0×10}6 _3.2×10−6 _4.3×10−8 48 2.2×10−5 _{3.4 3.1}×105 _5.1×10−6 _1.4×10−7 72 3.2×10−5 _{3.1 2.1}×105 _7.8×10−6 _2.1×10−7 168 1.2×10−4 _{3.0 5.1}×104 _2.9×10−5 _8.6×10−7 0 _1x106 2x106 3x106 4x106 0 1x106 2x106 3x106 4x106 54 H z

-Z

''

/

Ω

c

m

2

Z

'

/

Ω

cm

2 50 mHz 10-3 10-2 10-1 100 101 102 103 104 105 103 104 105 106 107

|Z

|

/

Ω

c

m

2

f / Hz

10-3 10-2 10-1 100 101 102 103 104 105 0 30 60 90

Sample E after 48 h in Na

₂

SO

₄

φ

/

°

f / Hz

Fig.6. ComparisonoftheexperimentalimpedanceplotsobtainedwithsampleEexposedto0.5MNa2SO4,aftera48-himmersiontime,withthebestfittedcurveobtained

byassumingw=22.2cm,c=2×1011_cm,ε

w=82andεc=8.

Onceporeisknown,resistivityprofilestakingintoaccountthe electrolyteinallporesmaybecalculatedaccordingtoEq.(1),in which()isreplacedby′_()definedas

′_()=

pore+ (ı)

1+_(ı)( −1) (9)

Fig.5comparesthesenew()−_profiles (emptysymbols) withthose reported inFig. 10 of Ref.[7] (fullsymbols), which werecalculatedbydirectlyusingthefitted(ı)and valuesand neglectingtheelectrolyteinthethroughpores.Clearly,takingpore intoaccountaffects(ı)onlymarginally,thusthelowerresistivity limit(ı)isessentiallyidenticalinthisnewcalculationandinthe previousone.Instead,foreachimmersiontime,theresistivityat =0calculatedaccordingtoEqs.(1)and(9)andbasedon′_()is

markedlylowerthanthatcalculatedaccordingtoEqs.(1)and(5)

andbasedon().

Additionaldifferencescausedbyusing′_{()insteadof()are:}

(i)amoreextendedregionwhere()isindependentof,next tothecoating/oxideinterface,and (ii)aprogressivedecreaseof (0)withincreasingimmersiontime.Thepresenceofinnerand outerlayersinorganicfilmswasexperimentallyshownbyKittel etal.[20]whohighlightedtheheterogeneityofthepropertiesof coatingsalongtheirthickness.

InspectionofTable1showsthatthetotalwateruptake (aver-aged along thecoating thickness), given byav+pore,remains below10−4_{,i.e.below0.01%,evenafter168hofimmersion.Such}

avalueissignificantlylowerthanvaluesoftenreportedinthe lit-eratureforvariouscoatingsmaterials(typicallybetween0.1%and 10%,seee.g.[11–13,19–22]).

Direct andreliable gravimetric datafor oursamplesarenot available.Inprevioussectionswediscussedreasonswhythewater uptakedatainTable1maybesignificantlyunderestimated. How-ever,itmustbestressedthat,althoughtheresultsofthefitting procedure are reported in part in terms of water uptake, e.g. (ı), what really matters is the conductivity, given by Eq. (1), and, with verygood approximation by Eq. (8). In the develop-mentofthepower-lawmodel(referredtoelectrolyte-penetrated coatings),()wasassumedtobedistributedalongthethickness accordingtoapowerlaw,andthecorrespondingresistivityand permittivitydistributionswerecalculatedaccordingly.Itmustbe realizedthat()isjustanintermediate inthecalculation.The modelmightbedirectlydescribedintermsof()andε(),both assumed to undergoa power-lawvariation, over a largeand a small(essentiallynegligible)range,respectively.Regressionwould thendirectlyprovide(ı)and values,allowingthecalculationof ()−profilesidenticaltothoseshowninthepresentpaper.In otherwords,thedetermined()−_profiles,e.g.thoseinFig.5,are

reliable,whereasthe()−maybeornotreliable,dependingon permselectivityeffectsandonthepresence/absenceofsignificant amountsofpolymer-boundedwater.

Analyses ofthe water uptake basedonthe evolution ofthe coatingcapacitancewithimmersiontimeoftenleadtoits overesti-mation,byasmallfactor,ascomparedwithgravimetricmethods. Since the permittivity of water does not change dramatically withtheconcentrationofionsdissolvedinit,estimatesbasedon capacitanceareintrinsicallylesssensitivetoselectiveuptakeof water/ionsthanourapproachrelyingonresistivityvariations.

4.3. Effectofcoatingformulationandelectrolytecomposition

TheimpedanceofcoatingsEandOwasmeasuredduring immer-sionin0.5MNa2SO4,during168h,andanalyzedusingthemodel

describedinRef.[7],withthesameapproachasdescribedabove for coating Eexposed to0.5M NaCl.CoatingO, less protective than coatingE, wasnotstudied inNaCl solutionbecausesigns ofcorrosionappearedrathersoonand,toaccountforthe corro-sionprocess, theproposedmodelwould needtobecompleted byincludingeitheradditionalcircuitelementsoranappropriate analyticalexpression.

Theagreementbetweenexperimentsandmodelwasgoodfor allimmersion times,although,as discussedbefore, divergences appeared at frequencies higher than 1kHz (which were there-fore not taken into account in the fitting),as shown in Fig. 6.

Tables2and3summarizethefittingresults,whicharecompared tothoseforthecoatingE/NaClsysteminFig.7.Clearly,thedifferent coating/solution combinations showsignificantly different time dependenciesofbothRporeand(ı).ForcoatingE,uponincreasing theimmersiontime,RporedecreasesinNaClsolution,butincreases inNa2SO4solution.ForcoatingOinNa2SO4solution,Rpore under-goesonlysmallvariations,initiallydecreasingand thenslightly increasing.ForcoatingE,uponincreasingtheimmersiontime,(ı) increasesrapidlyinNaClsolutionandremainsroughlyconstantat amuchlowervalueinNa2SO4 solution.ForcoatingOinNa2SO4

solution,(ı)isinitiallymuchhigherthanforcoatingEandthen increasesslowlywhenimmersiontimeincreases.

TheseresultssuggestthatcoatingEisintrinsicallyless defec-tivethancoatingO,henceitslowerwateruptakeandsomewhat higherRporevalueatshortimmersiontime.CoatingOundergoes thenonlyminorchanges,i.e.itdoesnotuptakemuchadditional water, nor significantamounts of sulfate ions diffuse fromthe external solutiontothesolutionin thepores.CoatingE shows divergingbehaviour,dependingontheanioninthetestsolution. Supposingthattheamountofwateruptakenbythecoatingisnot

168 144 120 96 72 48 24 0 0 1x106 2x106 3x106 4x106

R

pore

/

Ω

cm

2

Immersion time / h

Coating E / NaCl Coating E / Na₂SO₄ Coating O / Na₂SO₄

a

168 144 120 96 72 48 24 0 2.0x10-5 4.0x10-5 6.0x10-5 8.0x10-5 1.0x10-4 1.2x10-4 Coating E / NaCl Coating E / Na₂SO₄ Coating O / Na₂SO₄ φ(δ)

/ dimensionless

Immersion time / h

b

Fig.7.DependenceofRporeand(ı)ontheimmersiontimeforthecoating/solution

combinationsindicatedonthefigure.Thelinesareonlyanaidfortheeye.

dramatically differentin the two cases [12], theRpore decrease and(ı)decreasemightactuallybetheresultoftheprogressive increaseinthechlorideconcentrationinthepores(witha result-ingdecreaseinresistivity).Suchaneffectwouldnotbeobservedin sulfatesolution,duetoamuchslowerdiffusionofthisanion.The increaseinRpore valueswithexposuretime,observedinNa2SO4

solution,isnotacommonphenomenon,butincreasingimpedances have been observed in other studies [13,23]. To explain the

Table2

Dependenceofthefittedparameters(ı), andRporeandofthecalculatedquantitiesavandporeontheimmersiontimein0.5MNa2SO4forcoatingE.

Immersiontimein0.5MNa2SO4/h (ı)/dimensionless /dimensionless Rpore/cm2 av/dimensionless pore/dimensionless

6 2.3×10−6 _{3.6 8.5×10}5 _5.3×10−7 _3.9×10−8 24 3.9×10−6 _{4.0 1.9}×106 _8.0×10−7 _1.8×10−8 48 1.6×10−6 _{3.9 2.5}×106 _3.5×10−7 _1.3×10−8 72 3.8×10−6 _{4.2 2.9}×106 _7.9×10−7 _1.1×10−8 168 2.2×10−6 _{4.2 2.9×10}6 _4.4×10−7 _1.1×10−8 Table3

Dependenceofthefittedparameters(ı), andRporeandofthecalculatedquantitiesavandporeontheimmersiontimein0.5MNa2SO4forcoatingO.

Immersiontimein0.5MNa2SO4/h (ı)/dimensionless /dimensionless Rpore/cm2 av/dimensionless pore/dimensionless

6 3.7×10−5 _{3.9 6.7}×105 _7.7×10−6 _4.9×10−8 24 2.8×10−5 _{3.4 6.7}×105 _6.5×10−6 _5.0×10−8 48 4.3×10−5 _{3.4 5.4}×105 _9.8×10−6 _6.2×10−8 120 4.4×10−5 _{3.2 7.8}×105 _1.0×10−5 _4.3×10−8 144 5.2×10−5 _{3.3 8.3×10}5 _1.2×10−5 _4.0×10−8 168 5.3×10−5 _{3.3 9.5×10}5 _1.2×10−5 _3.5×10−8

experimentalobservations,eitherafurtherwater-induced cross-linkingofthecoatingmaterialor,lessprobably,aporeshrinkingas aconsequenceofcoatingswellingmaybehypothesized. Indepen-dentevidenceallowingtoassesswhichphenomenonpredominates isnotavailable.

5. Conclusions

The“power-lawmodel”, whose applicationtoanti-corrosion coatingshad been proposedin Ref. [7], hasbeenrevisited and employedtoanalyzenewexperimentaldata.

Ithasbeenshownthataninaccurateknowledgeoftheresistivity ofthedrycoatingmaterialcisunlikelytoaffectthequalityofthe agreementbetweenmodelandexperimentaldata,northevaluesof theregressedparameters,atleastaslongascislarge.Instead,an erroneousassumptionabouttheresistivityoftheelectrolyte(w) withinthecoatingporeshasamajorimpactontheestimatedwater uptake.If,asithasbeenoftenreported,thediffusionofionsinto thecoatingisslowerthatwaterdiffusion,thenbothwandwill beunderestimated,possiblybyalargefactor.

Theeffectof“throughpores”and“shortpores”hasbeentaken simultaneouslyintoaccounttocalculateresistivityprofiles.

Finally,itwasshownthattheevolutionofthecoatingproperties withimmersiontimedependsbothonthecoatingmaterial,e.g. onitsmicrostructure,andontheelectrolyte,e.g.theabilityofits anionstodiffuseintothecoating.

Acknowledgments

Theexperimentaldatawereobtainedintheframeworkofthe SMILEproject(SurfaceMonoInnovativeLayerforEnvironment), withthefinancialsupportoftheDGCIS(DirectionGénéraledela Compétitivité,del’IndustrieetdesServices).N.Pébèrethanksthe partnersoftheproject:Mapaero(Pamiers),Rescoll(Bordeaux), Air-bus(Toulouse),Dassault(Paris),EADSIW(Suresnes),l’Electrolyse (Bordeaux),and thelaboratoriesLCPOand US2B(Universitéde Bordeaux).

References

[1]L.Beaunier,I.Epelboin,J.C.Lestrade,H.Takenouti,Etudeélectrochimiqueet parmicroscopieélectroniqueabalayageduferrecouvertdepeinture,Surf. Technol.4(1976)237.

[2]M.E.Orazem,I.Frateur,B.Tribollet,V.Vivier,S.Marcelin,N.Pébère,A.L.Bunge, E.A.White,D.P.Riemer,M.Musiani,Dielectricpropertiesofmaterialsshowing constant-phase-element(CPE)impedanceresponse,J.Electrochem.Soc.160 (2013)C215.

[3]D.M. Brasher, A.H. Kingsbury, Electrical measurements in the study of immersedpaintcoatingsonmetal.I.Comparisonbetweencapacitanceand gravimetricmethodsofestimatingwater-uptake,J.Appl.Chem.4(1954) 62.

[4]G.J.Brug,A.L.G.vandenEeden,M.Sluyters-Rehbach,J.H.Sluyters,The analy-sisofelectrodeimpedancescomplicatedbythepresenceofaconstantphase element,J.Electroanal.Chem.176(1984)275.

[5]C.H.Hsu,F.Mansfeld,Concerningtheconversionoftheconstantphaseelement parameterY-0intoacapacitance,Corrosion57(2001)747.

[6]B. Hirschorn,M.E.Orazem, B. Tribollet, V.Vivier,I. Frateur,M.Musiani, Determinationofeffective capacitanceandfilmthickness from constant-phase-elementparameters,Electrochim.Acta55(2010)6218.

[7]S. Amand, M. Musiani, M.E. Orazem, N. Pébère, B. Tribollet, V. Vivier, Constant-phase-elementbehaviorcausedbyinhomogeneouswateruptakein anti-corrosioncoatings,Electrochim.Acta87(2013)693.

[8]B. Hirschorn,M.E.Orazem, B. Tribollet, V.Vivier,I. Frateur,M.Musiani, Constant-phase-elementbehaviorcausedbyresistivitydistributionsinfilms: 1.Theory,J.Electrochem.Soc.157(2010)C452.

[9]M.Musiani,M.E.Orazem,N.Pébère,B.Tribollet,V.Vivier, Constant-phase-elementbehaviorcausedbycoupledresistivityandpermittivitydistributions infilms,J.Electrochem.Soc.158(2011)C424.

[10]B. Hirschorn,M.E.Orazem, B. Tribollet, V.Vivier,I. Frateur,M.Musiani, Constant-phase-elementbehaviorcausedbyresistivitydistributionsinfilms: 2.Applications,J.Electrochem.Soc.157(2010)C458.

[11]V.B.Miˇskovi ´c-Stankovi ´c,D.M.Draˇzi ´c,M.J.Teodorovi ´c,Electrolyte penetra-tionthroughepoxycoatingselectrodepositedonsteel,Corros.Sci.37(1995) 241.

[12]V.B.Miˇskovi ´c-Stankovi ´c,D.M.Draˇzi ´c,Z.Kaˇcarevi ´c-Popovi ´c,Thesorption char-acteristicsofepoxycoatingselectrodepositedonsteelduringexposureto differentcorrosiveagents,Corros.Sci.38(1996)1513.

[13]C.LePen,C.Lacabanne,N.Pébère,Characterisationofwater-basedcoatingsby electrochemicalimpedancespectroscopy,Prog.Org.Coat.46(2003)77.

[14]A.R.Blythe,Electricalresistivitymeasurementsofpolymermaterials,Polym. Test.4(1984)195.

[15]M.E.Baird,NatureofDCconductivityinpolyamides,J.PolymerSci.A-28(1970) 739.

[16]B.R.Hinderliter,S.G.Croll,D.E.Tallman,Q.Su,G.P.Bierwagen,Interpretation ofEISdatafromacceleratedexposureofcoatedmetalsbasedonmodelingof coatingphysicalproperties,Electrochim.Acta51(2006)4505.

[17]A.S.Castela,A.M.Simoes,Assessmentofwateruptakeincoilcoatingsby capac-itancemeasurements,Prog.Org.Coat.46(2003)55.

[18]J.M.Hu,J.Q.Zhang,C.N.Cao,DeterminationofwateruptakeanddiffusionofCl− ioninepoxyprimeronaluminumalloysinNaClsolutionbyelectrochemical impedancespectroscopy,Prog.Org.Coat.46(2003)273.

[19]R.G.Duarte,S.González,A.S.Castela,M.G.S.Ferreira,R.M.Souto,Sensing polymerinhomogeneityincoatedmetalsduringtheearlystagesofcoating degradation,Prog.Org.Coat.74(2012)365.

[20]J.Kittel,N.Celati,M.Keddam,H.Takenouti,Newmethodsforthestudyof organiccoatingsbyEIS:newinsightsintoattachedandfreefilms,Prog.Org. Coat.41(2001)93.

[21]J.H.Park,G.D.Lee,H.Ooshige,A.Nishikata,T.Tsuru,Monitoringofwateruptake inorganiccoatingsundercyclicwet–drycondition,Corros.Sci.45(2003)1881.

[22]R.G.Duarte,A.S.Castela,M.G.S.Ferreira,Anewmodelforestimationofwater uptakeofanorganiccoatingbyEIS:thetortuosityporemodel,Prog.Org.Coat. 65(2009)197.

[23]M.C.S.S.Macedo,I.C.P.Margarit-Mattos,F.L.Fragata,J.-B.Jorcin,N.Pébère,O.R. Mattos,Contributiontoabetterunderstandingofdifferentbehaviourpatterns observedwithorganiccoatingsevaluatedbyelectrochemicalimpedance spec-troscopy,Corros.Sci.51(2009)1322.